Finite Group Databasebeta

← C2×#11754826 #14482593

Subgroups — C2×#11754826 #14482593

Order 1920.

3800 conjugacy classes of subgroups.

The subgroup lattice has 1040 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×D15C211yesmaximal, characteristic, complemented
2C22×#6782C211yesmaximal, characteristic, complemented
3C2×C5×#939C211yesmaximal, characteristic, complemented
4C2×C3×#4081C211yesmaximal, characteristic, complemented
5C2×#91573C211yesmaximal, characteristic, complemented
6C2×#91573C211yesmaximal, characteristic, complemented
7C2×#91561C211yesmaximal, characteristic, complemented
8C2×#91558C211yesmaximal, characteristic, complemented
9C2×#91556C211yesmaximal, characteristic, complemented
10C22×#6667C211yesmaximal, characteristic, complemented
11C2×#91526C211yesmaximal, characteristic, complemented
12#11754826C2116yesmaximal, direct product factor
13C2×#91433C211yesmaximal, characteristic, complemented
14C2×#91420C211yesmaximal, characteristic, complemented
15C2×#91406C211yesmaximal, characteristic, complemented
16C2×#91377C211yesmaximal, characteristic, complemented
17C2×#65944—31nomaximal, Hall
18C24×D15C2211yescharacteristic
19C24×D15C2211yescharacteristic
20C22×C3×C5×D4C2211yescharacteristic
21C22×#1220C2211yescharacteristic
22C22×#1220C2211yescharacteristic
23C2×D4×D15—28no—
24C2×D4×D15C2218yescomplemented
25C22×D60C2211yescharacteristic
26C22×C4×D15C2211yescharacteristic
27C22×C5×#67C2211yescharacteristic, complemented
28C22×C5×#67C2211yescharacteristic, complemented
29C23×C5×Dic3C2211yescharacteristic, complemented
30C23×C3×Dic5C2211yescharacteristic, complemented
31C22×#1204C2211yescharacteristic, complemented
32C22×#1203C2211yescharacteristic
33C22×#1203C2211yescharacteristic, complemented
34C22×#1203C2211yescharacteristic, complemented
35C22×#1200C2211yescharacteristic, complemented
36C22×#1200C2211yescharacteristic, complemented
37C2×#6782—28no—
38C2×#6782C2218yescomplemented
39C22×D3×Dic5C2211yescharacteristic, complemented
40C2×C5×#217C2211yescharacteristic, complemented
41C5×#939C2218yescomplemented
42C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
44C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
45C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
46C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
47C3×#4081C2218yescomplemented
48C2×C3×#683C2211yescharacteristic, complemented
49C2×C3×#683C2211yescharacteristic, complemented
50#91573C2218yescomplemented
51#91573C2218yescomplemented
52#91561C2218yescomplemented
53#91558C2218yescomplemented
54#91556C2218yescomplemented
55C2×#6669C2211yescharacteristic, complemented
56C2×#6667C2211yescharacteristic
57C2×#6667C2211yescharacteristic
58C2×#6667C2211yescharacteristic
59C2×#6667C2218yescomplemented
60C2×#6667C2211yescharacteristic, complemented
61C2×#6667C2211yescharacteristic, complemented
62C2×#6667C2211yescharacteristic, complemented
63C2×#6667C2211yescharacteristic, complemented
64C2×Dic3×Dic5C2211yescharacteristic, complemented
65#91526C2218yescomplemented
66#91433C2218yescomplemented
67#91420C2218yescomplemented
68#91406C2218yescomplemented
69#91377C2218yescomplemented
70C2×#5654—51nomaximal, Hall
71C22×#711—31no—
72C22×D4×D5—31no—
73C2×C5×#121—31no—
74C2×#4085—31no—
75C2×#4083—31no—
76C2×#4083—31no—
77C2×#4081D311yescharacteristic, complemented
78C2×C4×C22⋊D5—31no—
79C22×#685—31no—
80#65944—316no—
81C2×#4042—31no—
82C2×#4040—31no—
83C2×#4031—31no—
84C2×#4030—31no—
85C2×#4027—31no—
86C2×D5×C22⋊C4—31no—
87C24×C3×C5C2311yescharacteristic
88C24×C3×C5C2311yescharacteristic
89C23×D15—24no—
90C23×D15—24no—
91C23×D15—24no—
92C23×D15—24no—
93C23×D15—42no—
94C23×D15—42no—
95C23×D15C2311yescharacteristic
96C23×D15C2314yes—
97C23×D15C2314yes—
98C23×D15C2311yescharacteristic
99C23×D15C2311yescharacteristic
100C23×C5×D3C2311yescharacteristic
101C2×C3×C5×D4—24no—
102C2×C3×C5×D4C2314yes—
103C22×C3×C4×C5C2311yescharacteristic
104C2×#1220—24no—
105C2×#1220D418yescomplemented
106C2×#1220C2314yes—
107C2×#1220C2314yes—
108C22×Dic15C2311yescharacteristic
109D4×D15—232no—
110C2×D60—24no—
111C2×D60C2314yes—
112C2×C4×D15—24no—
113C2×C4×D15C2314yes—
114C2×C5×#67—24no—
115C2×C5×#67—42no—
116C2×C5×#67C2314yescomplemented
117C2×C5×#67C2314yescomplemented
118C22×C5×Dic3—42no—
119C22×C5×Dic3C2311yescharacteristic
120C22×C5×Dic3C2311yescharacteristic
121C22×C5×Dic3C2311yescharacteristic
122C22×C5×Dic3C2314yescomplemented
123C22×C3×Dic5—24no—
124C22×C3×Dic5C2311yescharacteristic
125C22×C3×Dic5C2311yescharacteristic
126C22×C3×Dic5C2311yescharacteristic
127C22×C3×Dic5C2311yescharacteristic
128C22×C3×Dic5C2314yescomplemented
129C2×#1204—24no—
130C2×#1204C2314yescomplemented
131C2×#1203—24no—
132C2×#1203—24no—
133C2×#1203—42no—
134C2×#1203C2314yes—
135C2×#1203C2314yescomplemented
136C2×#1203C2314yescomplemented
137C2×#1200—24no—
138C2×#1200—42no—
139C2×#1200C2314yescomplemented
140C2×#1200C2314yescomplemented
141#6782—232no—
142C2×D3×Dic5—24no—
143C2×D3×Dic5C2314yescomplemented
144C5×#217C2314yescomplemented
145C5×(C2×D3)⋊C4C2314yescomplemented
146C5×Dic3⋊C4C2314yescomplemented
147C3×C22⋊Dic5C2314yescomplemented
148C3×C22⋊Dic5C2314yescomplemented
149C3×C22⋊Dic5C2314yescomplemented
150C3×#683C2314yescomplemented
151C3×#683C2314yescomplemented
152#6669C2314yescomplemented
153#6667C2314yes—
154#6667C2314yes—
155#6667C2314yes—
156#6667C2314yescomplemented
157#6667C2314yescomplemented
158#6667C2314yescomplemented
159#6667C2314yescomplemented
160Dic3×Dic5C2314yescomplemented
161C22×D3×D4—51no—
162C22×#235—51no—
163C2×C3×#123—51no—
164C2×#939D511yescharacteristic, complemented
165C22×(C2×D3)⋊C4—51no—
166#5654—516no—
167C2×#896—51no—
168C2×#895—51no—
169C2×#894—51no—
170C2×#893—51no—
171C2×#885—51no—
172C2×#884—51no—
173C2×#882—51no—
174C2×#882—51no—
175C2×#67⋊C4—51no—
176C2×D3×C22⋊C4—51no—
177C24×D5—31no—
178C24×D5—31no—
179C22×C5×D4—31no—
180C22×C5×D4—31no—
181C22×C5×D4C2×D311yescharacteristic
182C23×C4×C5—31no—
183C22×C22⋊D5—31no—
184C22×C22⋊D5—31no—
185C22×C22⋊D5—31no—
186C22×C22⋊D5—31no—
187C22×C22⋊D5—31no—
188C23×Dic5—31no—
189C23×Dic5C2×D311yescharacteristic, complemented
190C2×#711—38no—
191C2×#711—68no—
192C2×D4×D5—38no—
193C2×D4×D5—68no—
194C22×D20—31no—
195C22×C4×D5—31no—
196C22×C4×D5—31no—
197C22×C4×D5—31no—
198C22×Dic10—31no—
199C5×#121—38no—
200C2×C5×C4⋊C4—31no—
201C2×C5×C22⋊C4—31no—
202C2×C5×C22⋊C4—31no—
203C2×C22⋊Dic5C2×D311yescharacteristic, complemented
204C2×C22⋊Dic5C2×D311yescharacteristic, complemented
205C2×C22⋊Dic5C2×D311yescharacteristic, complemented
206#4085—38no—
207#4083—38no—
208#4083—38no—
209#4081C2×D318yescomplemented
210C4×C22⋊D5—38no—
211C2×#685—31no—
212C2×#685—31no—
213C2×#685—31no—
214C2×#685—31no—
215C2×#685—31no—
216C2×#685—31no—
217C2×#685—31no—
218C2×#685—38no—
219C2×#683—31no—
220C2×#683C2×D311yescharacteristic, complemented
221C2×#683C2×D311yescharacteristic, complemented
222C2×C4×Dic5—31no—
223#4042—38no—
224#4040—38no—
225#4031—38no—
226#4030—38no—
227#4027—38no—
228D5×C22⋊C4—38no—
229C2×#546—151noSylow
230C23×C3×C5—22no—
231C23×C3×C5—22no—
232C23×C3×C5—22no—
233C23×C3×C5—22no—
234C23×C3×C5—22no—
235C23×C3×C5C2×D414yes—
236C23×C3×C5C2412yes—
237C23×C3×C5C2412yes—
238C23×C3×C5C2411yescharacteristic
239C22×D15—22no—
240C22×D15—22no—
241C22×D15—22no—
242C22×D15—22no—
243C22×D15—22no—
244C22×D15—28no—
245C22×D15—22no—
246C22×D15—22no—
247C22×D15—28no—
248C22×D15—28no—
249C22×D15—28no—
250C22×D15—44no—
251C22×D15—44no—
252C22×D15—416no—
253C22×D15—416no—
254C22×D15C2×D414yes—
255C22×D15#4114yescomplemented
256C22×D15C2412yes—
257C22×D15C2412yes—
258C22×D15C2412yes—
259C22×C5×D3—22no—
260C22×C5×D3—22no—
261C22×C5×D3—22no—
262C22×C5×D3C2412yes—
263C3×C5×D4—28no—
264C2×C3×C4×C5—22no—
265C2×C3×C4×C5C2412yes—
266#1220—28no—
267#1220C2×D4116yescomplemented
268C2×Dic15C2×D414yes—
269C2×Dic15C2412yes—
270D60—28no—
271C4×D15—28no—
272C5×#67—28no—
273C5×#67—44no—
274C2×C5×Dic3—22no—
275C2×C5×Dic3—22no—
276C2×C5×Dic3—22no—
277C2×C5×Dic3—44no—
278C2×C5×Dic3C2412yes—
279C2×C5×Dic3C2412yes—
280C2×C5×Dic3C2412yes—
281C2×C3×Dic5—22no—
282C2×C3×Dic5—28no—
283C2×C3×Dic5—22no—
284C2×C3×Dic5—22no—
285C2×C3×Dic5—22no—
286C2×C3×Dic5C2412yes—
287C2×C3×Dic5C2412yes—
288C2×C3×Dic5C2412yes—
289C2×C3×Dic5C2412yes—
290#1204—28no—
291#1203—28no—
292#1203—28no—
293#1203—44no—
294#1200—28no—
295#1200—44no—
296D3×Dic5—28no—
297C24×D3—51no—
298C24×D3—51no—
299C22×C3×D4C2×D511yescharacteristic
300C23×C3×C4—51no—
301C22×#67—51no—
302C22×#67—51no—
303C22×#67C2×D511yescharacteristic, complemented
304C22×#67C2×D511yescharacteristic, complemented
305C23×Dic3C2×D511yescharacteristic, complemented
306C2×D3×D4—58no—
307C2×D3×D4—108no—
308C2×#235—58no—
309C2×#235—108no—
310C22×D12—51no—
311C22×D12—51no—
312C22×D12—51no—
313C22×D12—51no—
314C22×C4×D3—51no—
315C22×C4×D3—51no—
316C22×C4×D3—51no—
317C22×C4×D3—51no—
318C22×Dic6—51no—
319C3×#123—58no—
320C2×C3×C4⋊C4—51no—
321C2×C3×C4⋊C4—51no—
322C2×C3×C22⋊C4—51no—
323C2×C3×C22⋊C4—51no—
324C2×C3×C22⋊C4—51no—
325C2×#217C2×D511yescharacteristic, complemented
326#939C2×D518yescomplemented
327C2×(C2×D3)⋊C4—51no—
328C2×(C2×D3)⋊C4—51no—
329C2×(C2×D3)⋊C4—51no—
330C2×(C2×D3)⋊C4—51no—
331C2×(C2×D3)⋊C4—51no—
332C2×(C2×D3)⋊C4—51no—
333C2×(C2×D3)⋊C4—51no—
334C2×(C2×D3)⋊C4—58no—
335C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
336C2×Dic3⋊C4—51no—
337C2×Dic3⋊C4C2×D511yescharacteristic, complemented
338C2×C4×Dic3—51no—
339#896—58no—
340#895—58no—
341#894—58no—
342#893—58no—
343#885—58no—
344#884—58no—
345#882—58no—
346#882—58no—
347#67⋊C4—58no—
348D3×C22⋊C4—58no—
349C24×C5—31no—
350C24×C5C22×D311yescharacteristic
351C24×C5C22×D311yescharacteristic
352C23×D5—31no—
353C23×D5—31no—
354C23×D5—31no—
355C23×D5—34no—
356C23×D5—34no—
357C23×D5—64no—
358C23×D5—64no—
359C23×D5—64no—
360C23×D5—64no—
361C23×D5—122no—
362C23×D5—122no—
363C2×C5×D4—24no—
364C2×C5×D4—34no—
365C2×C5×D4—34no—
366C2×C5×D4—64no—
367C2×C5×D4—122no—
368C2×C5×D4C22×D314yes—
369C22×C4×C5—31no—
370C22×C4×C5—31no—
371C22×C4×C5—31no—
372C22×C4×C5—34no—
373C22×C4×C5—122no—
374C22×C4×C5C22×D311yescharacteristic
375C2×C22⋊D5—38no—
376C2×C22⋊D5—34no—
377C2×C22⋊D5—34no—
378C2×C22⋊D5—34no—
379C2×C22⋊D5—34no—
380C2×C22⋊D5—34no—
381C2×C22⋊D5—64no—
382C2×C22⋊D5—64no—
383C2×C22⋊D5—64no—
384C2×C22⋊D5—122no—
385C22×Dic5—24no—
386C22×Dic5—31no—
387C22×Dic5—34no—
388C22×Dic5—64no—
389C22×Dic5C22×D311yescharacteristic
390C22×Dic5C22×D311yescharacteristic
391C22×Dic5C22×D311yescharacteristic
392C22×Dic5C22×D311yescharacteristic
393C22×Dic5C22×D314yescomplemented
394#711—632no—
395D4×D5—632no—
396C2×D20—34no—
397C2×D20—64no—
398C2×C4×D5—34no—
399C2×C4×D5—34no—
400C2×C4×D5—34no—
401C2×C4×D5—64no—
402C2×C4×D5—64no—
403C2×C4×D5—122no—
404C2×Dic10—34no—
405C2×Dic10—64no—
406C5×C4⋊C4—34no—
407C5×C22⋊C4—34no—
408C5×C22⋊C4—34no—
409C22⋊Dic5C22×D314yescomplemented
410C22⋊Dic5C22×D314yescomplemented
411C22⋊Dic5C22×D314yescomplemented
412#685—34no—
413#685—34no—
414#685—34no—
415#685—34no—
416#685—34no—
417#685—34no—
418#685—34no—
419#683—34no—
420#683C22×D314yescomplemented
421#683C22×D314yescomplemented
422C4×Dic5—34no—
423C22×#41—151no—
424C23×D4—151no—
425#546—1516no—
426C2×#124—151no—
427C2×#123—51no—
428C2×#123—151no—
429C2×C22⋊Q8—151no—
430C2×#121—31no—
431C2×#121—151no—
432C2×#121—151no—
433C2×#120—151no—
434C2×#120—151no—
435C2×C4×D4—151no—
436C2×C4×D4—151no—
437C22×C22⋊C4—151no—
438C22×C22⋊C4—151no—
439C22×C3×C5—28no—
440C22×C3×C5—22no—
441C22×C3×C5—22no—
442C22×C3×C5—22no—
443C22×C3×C5—22no—
444C22×C3×C5—22no—
445C22×C3×C5—44no—
446C22×C3×C5C22×D414yes—
447C22×C3×C5C22×D412yes—
448C22×C3×C5C2×#4112yes—
449C22×C3×C5H(5,𝔽2)12yes—
450C22×C3×C5C2511yescharacteristic
451C2×D15—28no—
452C2×D15—28no—
453C2×D15—22no—
454C2×D15—22no—
455C2×D15—22no—
456C2×D15—22no—
457C2×D15—22no—
458C2×D15—22no—
459C2×D15—22no—
460C2×D15—416no—
461C2×D15—416no—
462C2×D15—44no—
463C2×D15C22×D414yes—
464C2×D15C2×#4114yescomplemented
465C2×C5×D3—22no—
466C2×C5×D3—22no—
467C2×C5×D3—22no—
468C2×C5×D3—44no—
469C3×C4×C5—22no—
470Dic15C22×D414yes—
471C3×Dic5—22no—
472C3×Dic5—22no—
473C3×Dic5—22no—
474C3×Dic5—22no—
475C5×Dic3—22no—
476C5×Dic3—22no—
477C5×Dic3—22no—
478C24×C3C22×D511yescharacteristic
479C24×C3C22×D511yescharacteristic
480C23×D3—51no—
481C23×D3—51no—
482C23×D3—51no—
483C23×D3—54no—
484C23×D3—54no—
485C23×D3—104no—
486C23×D3—104no—
487C23×D3—104no—
488C23×D3—104no—
489C23×D3—202no—
490C23×D3—202no—
491C23×D3C22×D511yescharacteristic
492C2×C3×D4—24no—
493C2×C3×D4C22×D514yes—
494C22×C3×C4—51no—
495C22×C3×C4—51no—
496C22×C3×C4—51no—
497C22×C3×C4—51no—
498C22×C3×C4—54no—
499C22×C3×C4—104no—
500C22×C3×C4C22×D511yescharacteristic
501C2×#67—24no—
502C2×#67—42no—
503C2×#67—58no—
504C2×#67—54no—
505C2×#67—54no—
506C2×#67—104no—
507C2×#67C22×D514yescomplemented
508C2×#67C22×D514yescomplemented
509C22×Dic3—42no—
510C22×Dic3—51no—
511C22×Dic3C22×D511yescharacteristic
512C22×Dic3C22×D511yescharacteristic
513C22×Dic3C22×D511yescharacteristic
514C22×Dic3C22×D514yescomplemented
515D3×D4—1032no—
516#235—1032no—
517C2×D12—54no—
518C2×D12—54no—
519C2×D12—54no—
520C2×D12—54no—
521C2×D12—104no—
522C2×D12—104no—
523C2×D12—104no—
524C2×D12—202no—
525C2×C4×D3—54no—
526C2×C4×D3—54no—
527C2×C4×D3—54no—
528C2×C4×D3—54no—
529C2×C4×D3—104no—
530C2×C4×D3—104no—
531C2×C4×D3—104no—
532C2×C4×D3—202no—
533C2×Dic6—54no—
534C2×Dic6—104no—
535C3×C4⋊C4—54no—
536C3×C4⋊C4—54no—
537C3×C22⋊C4—54no—
538C3×C22⋊C4—54no—
539C3×C22⋊C4—54no—
540#217C22×D514yescomplemented
541(C2×D3)⋊C4—54no—
542(C2×D3)⋊C4—54no—
543(C2×D3)⋊C4—54no—
544(C2×D3)⋊C4—54no—
545(C2×D3)⋊C4—54no—
546(C2×D3)⋊C4—54no—
547(C2×D3)⋊C4—54no—
548(C2×D3)⋊C4C22×D514yescomplemented
549Dic3⋊C4—54no—
550Dic3⋊C4C22×D514yescomplemented
551C4×Dic3—54no—
552C23×C5—22no—
553C23×C5—22no—
554C23×C5—22no—
555C23×C5—22no—
556C23×C5—22no—
557C23×C5—32no—
558C23×C5—62no—
559C23×C5—62no—
560C23×C5—62no—
561C23×C5D3×D414yes—
562C23×C5C23×D312yes—
563C23×C5C23×D312yes—
564C23×C5C23×D311yescharacteristic
565C22×D5—34no—
566C22×D5—34no—
567C22×D5—32no—
568C22×D5—32no—
569C22×D5—32no—
570C22×D5—68no—
571C22×D5—68no—
572C22×D5—68no—
573C22×D5—62no—
574C22×D5—62no—
575C22×D5—62no—
576C22×D5—62no—
577C22×D5—62no—
578C22×D5—68no—
579C22×D5—62no—
580C22×D5—62no—
581C22×D5—124no—
582C22×D5—124no—
583C22×D5—1216no—
584C22×D5—1216no—
585C5×D4—28no—
586C5×D4—68no—
587C5×D4—124no—
588C2×C4×C5—22no—
589C2×C4×C5—32no—
590C2×C4×C5—32no—
591C2×C4×C5—32no—
592C2×C4×C5—62no—
593C2×C4×C5—62no—
594C2×C4×C5—62no—
595C2×C4×C5—124no—
596C2×C4×C5C23×D312yes—
597C22⋊D5—316no—
598C22⋊D5—68no—
599C22⋊D5—68no—
600C22⋊D5—68no—
601C22⋊D5—124no—
602C2×Dic5—22no—
603C2×Dic5—22no—
604C2×Dic5—28no—
605C2×Dic5—22no—
606C2×Dic5—22no—
607C2×Dic5—34no—
608C2×Dic5—32no—
609C2×Dic5—68no—
610C2×Dic5C23×D312yes—
611C2×Dic5C23×D312yes—
612C2×Dic5C23×D312yes—
613C2×Dic5C23×D312yes—
614D20—68no—
615C4×D5—68no—
616C4×D5—68no—
617C4×D5—124no—
618Dic10—68no—
619C25—151no—
620C25—151no—
621C2×#41—158no—
622C2×#41—308no—
623C22×Q8—151no—
624C22×D4—31no—
625C22×D4—31no—
626C22×D4—151no—
627C22×D4—151no—
628C22×D4—151no—
629C22×D4—151no—
630C22×D4—151no—
631C22×D4—158no—
632C22×D4—151no—
633C22×D4—308no—
634C22×D4D3×D511yescharacteristic
635C23×C4—31no—
636C23×C4—51no—
637C23×C4—151no—
638C23×C4—151no—
639C23×C4—151no—
640C23×C4—151no—
641#124—158no—
642#123—58no—
643#123—158no—
644C22⋊Q8—158no—
645#121—38no—
646#121—158no—
647#121—158no—
648#120—158no—
649#120—158no—
650C4×D4—158no—
651C4×D4—158no—
652C2×C4⋊C4—31no—
653C2×C4⋊C4—51no—
654C2×C4⋊C4—51no—
655C2×C4⋊C4—151no—
656C2×C22⋊C4—31no—
657C2×C22⋊C4—31no—
658C2×C22⋊C4—51no—
659C2×C22⋊C4—51no—
660C2×C22⋊C4—51no—
661C2×C22⋊C4—158no—
662C2×C22⋊C4—151no—
663C2×C22⋊C4—151no—
664C2×C22⋊C4—151no—
665C2×C22⋊C4—151no—
666C2×C22⋊C4—151no—
667C2×C22⋊C4—158no—
668C2×C22⋊C4—151no—
669C2×C22⋊C4—151no—
670C2×C42—151no—
671C2×C3×C5—24no—
672C2×C3×C5—42no—
673C2×C3×C5#54614yescomplemented
674C2×C3×C5C23×D411yescharacteristic
675C2×C3×C5C22×#4111yescharacteristic
676C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
677D15—24no—
678D15—24no—
679D15—42no—
680C5×D3—42no—
681C23×C3—22no—
682C23×C3—22no—
683C23×C3—22no—
684C23×C3—22no—
685C23×C3—22no—
686C23×C3D4×D514yes—
687C23×C3C23×D512yes—
688C23×C3C23×D512yes—
689C23×C3C23×D511yescharacteristic
690C22×D3—22no—
691C22×D3—22no—
692C22×D3—22no—
693C22×D3—54no—
694C22×D3—54no—
695C22×D3—52no—
696C22×D3—52no—
697C22×D3—52no—
698C22×D3—108no—
699C22×D3—108no—
700C22×D3—108no—
701C22×D3—102no—
702C22×D3—102no—
703C22×D3—102no—
704C22×D3—102no—
705C22×D3—102no—
706C22×D3—108no—
707C22×D3—102no—
708C22×D3—102no—
709C22×D3—204no—
710C22×D3—204no—
711C22×D3—2016no—
712C22×D3—2016no—
713C22×D3C23×D512yes—
714C3×D4—28no—
715C2×C3×C4—22no—
716C2×C3×C4—52no—
717C2×C3×C4—52no—
718C2×C3×C4—52no—
719C2×C3×C4—52no—
720C2×C3×C4—102no—
721C2×C3×C4—102no—
722C2×C3×C4—108no—
723C2×C3×C4—102no—
724C2×C3×C4—102no—
725C2×C3×C4C23×D512yes—
726#67—28no—
727#67—44no—
728#67—516no—
729#67—108no—
730C2×Dic3—22no—
731C2×Dic3—22no—
732C2×Dic3—22no—
733C2×Dic3—44no—
734C2×Dic3—54no—
735C2×Dic3—52no—
736C2×Dic3C23×D512yes—
737C2×Dic3C23×D512yes—
738C2×Dic3C23×D512yes—
739D12—108no—
740D12—108no—
741D12—108no—
742D12—204no—
743C4×D3—108no—
744C4×D3—108no—
745C4×D3—108no—
746C4×D3—204no—
747Dic6—108no—
748C22×C5—28no—
749C22×C5—22no—
750C22×C5—22no—
751C22×C5—22no—
752C22×C5—22no—
753C22×C5—22no—
754C22×C5—44no—
755C22×C5—62no—
756C22×C5—62no—
757C22×C5—62no—
758C22×C5—124no—
759C22×C5C2×D3×D414yes—
760C22×C5C2×D3×D412yes—
761C22×C5D3×#4112yes—
762C22×C5#100912yes—
763C22×C5C24×D311yescharacteristic
764C2×D5—34no—
765C2×D5—34no—
766C2×D5—68no—
767C2×D5—68no—
768C2×D5—62no—
769C2×D5—62no—
770C2×D5—62no—
771C2×D5—62no—
772C2×D5—62no—
773C2×D5—62no—
774C2×D5—62no—
775C2×D5—1216no—
776C2×D5—1216no—
777C2×D5—124no—
778C4×C5—22no—
779C4×C5—62no—
780C4×C5—62no—
781C4×C5—62no—
782Dic5—22no—
783Dic5—22no—
784Dic5—22no—
785Dic5—22no—
786Dic5—34no—
787C24—31no—
788C24—151no—
789C24—151no—
790C24—151no—
791C24—154no—
792C24—154no—
793C24—304no—
794C24—304no—
795C24—304no—
796C24—304no—
797C24—602no—
798C24—602no—
799C24C2×D3×D511yescharacteristic
800C24C2×D3×D511yescharacteristic
801#41—3032no—
802C2×Q8—154no—
803C2×Q8—304no—
804C2×D4—24no—
805C2×D4—34no—
806C2×D4—34no—
807C2×D4—64no—
808C2×D4—122no—
809C2×D4—154no—
810C2×D4—154no—
811C2×D4—154no—
812C2×D4—158no—
813C2×D4—154no—
814C2×D4—154no—
815C2×D4—154no—
816C2×D4—304no—
817C2×D4—304no—
818C2×D4—304no—
819C2×D4—304no—
820C2×D4—3032no—
821C2×D4—602no—
822C2×D4C2×D3×D514yes—
823C22×C4—31no—
824C22×C4—31no—
825C22×C4—31no—
826C22×C4—34no—
827C22×C4—54no—
828C22×C4—51no—
829C22×C4—51no—
830C22×C4—51no—
831C22×C4—51no—
832C22×C4—104no—
833C22×C4—122no—
834C22×C4—154no—
835C22×C4—154no—
836C22×C4—154no—
837C22×C4—151no—
838C22×C4—154no—
839C22×C4—304no—
840C22×C4—304no—
841C22×C4—304no—
842C22×C4—602no—
843C22×C4C2×D3×D511yescharacteristic
844C4⋊C4—34no—
845C4⋊C4—54no—
846C4⋊C4—54no—
847C4⋊C4—154no—
848C22⋊C4—34no—
849C22⋊C4—34no—
850C22⋊C4—54no—
851C22⋊C4—54no—
852C22⋊C4—54no—
853C22⋊C4—154no—
854C22⋊C4—154no—
855C22⋊C4—154no—
856C22⋊C4—154no—
857C22⋊C4—154no—
858C22⋊C4—154no—
859C22⋊C4—154no—
860C42—154no—
861C3×C5C2×#54611yescharacteristic, complemented, Hall
862C22×C3—28no—
863C22×C3—22no—
864C22×C3—22no—
865C22×C3—22no—
866C22×C3—22no—
867C22×C3—22no—
868C22×C3—44no—
869C22×C3C2×D4×D514yes—
870C22×C3C2×D4×D512yes—
871C22×C3#414412yes—
872C22×C3D5×#4112yes—
873C22×C3C24×D511yescharacteristic
874C2×D3—22no—
875C2×D3—22no—
876C2×D3—22no—
877C2×D3—44no—
878C2×D3—54no—
879C2×D3—54no—
880C2×D3—108no—
881C2×D3—108no—
882C2×D3—102no—
883C2×D3—102no—
884C2×D3—102no—
885C2×D3—102no—
886C2×D3—102no—
887C2×D3—102no—
888C2×D3—102no—
889C2×D3—2016no—
890C2×D3—2016no—
891C2×D3—204no—
892C3×C4—22no—
893C3×C4—102no—
894C3×C4—102no—
895C3×C4—102no—
896C3×C4—102no—
897Dic3—22no—
898Dic3—22no—
899Dic3—22no—
900Dic3—54no—
901C2×C5—24no—
902C2×C5—42no—
903C2×C5—122no—
904C2×C5#565414yescomplemented
905C2×C5C22×D3×D411yescharacteristic
906C2×C5C2×D3×#4111yescharacteristic
907C2×C5C2×#100911yescharacteristic
908D5—64no—
909D5—64no—
910D5—122no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—32no—
917C23—62no—
918C23—62no—
919C23—62no—
920C23—154no—
921C23—154no—
922C23—152no—
923C23—152no—
924C23—152no—
925C23—308no—
926C23—308no—
927C23—308no—
928C23—302no—
929C23—302no—
930C23—302no—
931C23—302no—
932C23—302no—
933C23—302no—
934C23—308no—
935C23—302no—
936C23—604no—
937C23—604no—
938C23—6016no—
939C23—6016no—
940C23#679014yes—
941C23C22×D3×D512yes—
942C23C22×D3×D512yes—
943C23C22×D3×D511yescharacteristic
944Q8—308no—
945D4—28no—
946D4—68no—
947D4—124no—
948D4—1516no—
949D4—308no—
950D4—308no—
951D4—308no—
952D4—308no—
953D4—604no—
954C2×C4—22no—
955C2×C4—32no—
956C2×C4—32no—
957C2×C4—32no—
958C2×C4—52no—
959C2×C4—52no—
960C2×C4—52no—
961C2×C4—52no—
962C2×C4—62no—
963C2×C4—62no—
964C2×C4—62no—
965C2×C4—102no—
966C2×C4—102no—
967C2×C4—102no—
968C2×C4—102no—
969C2×C4—108no—
970C2×C4—124no—
971C2×C4—154no—
972C2×C4—152no—
973C2×C4—308no—
974C2×C4—308no—
975C2×C4—308no—
976C2×C4—604no—
977C2×C4C22×D3×D512yes—
978C2×C3—24no—
979C2×C3—42no—
980C2×C3#6594414yescomplemented
981C2×C3C22×D4×D511yescharacteristic
982C2×C3C2×#414411yescharacteristic
983C2×C3C2×D5×#4111yescharacteristic
984D3—42no—
985D3—104no—
986D3—104no—
987D3—202no—
988C5C2×#565411yescharacteristic, complemented, Sylow
989C22—28no—
990C22—22no—
991C22—22no—
992C22—22no—
993C22—22no—
994C22—22no—
995C22—44no—
996C22—62no—
997C22—62no—
998C22—62no—
999C22—124no—
1000C22—154no—
1001C22—154no—
1002C22—302no—
1003C22—308no—
1004C22—308no—
1005C22—302no—
1006C22—302no—
1007C22—302no—
1008C22—302no—
1009C22—302no—
1010C22—302no—
1011C22—6016no—
1012C22—6016no—
1013C22—604no—
1014C22#9202412yes—
1015C22#9202712yes—
1016C22C2×#679014yes—
1017C22C2×#679012yes—
1018C22C23×D3×D511yescharacteristic
1019C4—22no—
1020C4—62no—
1021C4—62no—
1022C4—62no—
1023C4—102no—
1024C4—102no—
1025C4—102no—
1026C4—102no—
1027C4—154no—
1028C3C2×#6594411yescharacteristic, complemented, Sylow
1029C2—24no—
1030C2—42no—
1031C2—122no—
1032C2—304no—
1033C2—304no—
1034C2—602no—
1035C2#1175482614yesdirect product factor
1036C2C2×#9202411yescharacteristic
1037C2C2×#9202711yescharacteristic
1038C2C22×#679011yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C24
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#546
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×D4×D15C2semidirect
2. C22×#6782C2semidirect
3. C2×C5×#939C2semidirect
4. C2×C3×#4081C2semidirect
5. C2×#91573C2semidirect
6. C2×#91573C2semidirect
7. C2×#91561C2semidirect
8. C2×#91558C2semidirect
9. C2×#91556C2semidirect
10. C22×#6667C2semidirect
11. C2×#91526C2semidirect
12. #11754826C2direct (N × H)
13. C2×#91433C2semidirect
14. C2×#91420C2semidirect
15. C2×#91406C2semidirect
16. C2×#91377C2semidirect
24. C2×D4×D15C22semidirect
27. C22×C5×#67C22semidirect
28. C22×C5×#67C22semidirect
29. C23×C5×Dic3C22semidirect
30. C23×C3×Dic5C22semidirect
31. C22×#1204C22semidirect
33. C22×#1203C22semidirect
34. C22×#1203C22semidirect
35. C22×#1200C22semidirect
36. C22×#1200C22semidirect
38. C2×#6782C22semidirect
39. C22×D3×Dic5C22semidirect
40. C2×C5×#217C22semidirect
41. C5×#939C22semidirect
42. C2×C5×(C2×D3)⋊C4C22semidirect
43. C2×C5×Dic3⋊C4C22semidirect
44. C2×C3×C22⋊Dic5C22semidirect
45. C2×C3×C22⋊Dic5C22semidirect
46. C2×C3×C22⋊Dic5C22semidirect
47. C3×#4081C22semidirect
48. C2×C3×#683C22semidirect
49. C2×C3×#683C22semidirect
50. #91573C22semidirect
51. #91573C22semidirect
52. #91561C22semidirect
53. #91558C22semidirect
54. #91556C22semidirect
55. C2×#6669C22semidirect
59. C2×#6667C22semidirect
60. C2×#6667C22semidirect
61. C2×#6667C22semidirect
62. C2×#6667C22semidirect
63. C2×#6667C22semidirect
64. C2×Dic3×Dic5C22semidirect
65. #91526C22semidirect
66. #91433C22semidirect
67. #91420C22semidirect
68. #91406C22semidirect
69. #91377C22semidirect
77. C2×#4081D3semidirect
105. C2×#1220D4semidirect
116. C2×C5×#67C23semidirect
117. C2×C5×#67C23semidirect
122. C22×C5×Dic3C23semidirect
128. C22×C3×Dic5C23semidirect
130. C2×#1204C23semidirect
135. C2×#1203C23semidirect
136. C2×#1203C23semidirect
139. C2×#1200C23semidirect
140. C2×#1200C23semidirect
143. C2×D3×Dic5C23semidirect
144. C5×#217C23semidirect
145. C5×(C2×D3)⋊C4C23semidirect
146. C5×Dic3⋊C4C23semidirect
147. C3×C22⋊Dic5C23semidirect
148. C3×C22⋊Dic5C23semidirect
149. C3×C22⋊Dic5C23semidirect
150. C3×#683C23semidirect
151. C3×#683C23semidirect
152. #6669C23semidirect
156. #6667C23semidirect
157. #6667C23semidirect
158. #6667C23semidirect
159. #6667C23semidirect
160. Dic3×Dic5C23semidirect
164. C2×#939D5semidirect
189. C23×Dic5C2×D3semidirect
203. C2×C22⋊Dic5C2×D3semidirect
204. C2×C22⋊Dic5C2×D3semidirect
205. C2×C22⋊Dic5C2×D3semidirect
209. #4081C2×D3semidirect
220. C2×#683C2×D3semidirect
221. C2×#683C2×D3semidirect
255. C22×D15#41semidirect
267. #1220C2×D4semidirect
303. C22×#67C2×D5semidirect
304. C22×#67C2×D5semidirect
305. C23×Dic3C2×D5semidirect
325. C2×#217C2×D5semidirect
326. #939C2×D5semidirect
335. C2×(C2×D3)⋊C4C2×D5semidirect
337. C2×Dic3⋊C4C2×D5semidirect
393. C22×Dic5C22×D3semidirect
409. C22⋊Dic5C22×D3semidirect
410. C22⋊Dic5C22×D3semidirect
411. C22⋊Dic5C22×D3semidirect
420. #683C22×D3semidirect
421. #683C22×D3semidirect
464. C2×D15C2×#41semidirect
507. C2×#67C22×D5semidirect
508. C2×#67C22×D5semidirect
514. C22×Dic3C22×D5semidirect
540. #217C22×D5semidirect
548. (C2×D3)⋊C4C22×D5semidirect
550. Dic3⋊C4C22×D5semidirect
673. C2×C3×C5#546semidirect
861. C3×C5C2×#546semidirect
904. C2×C5#5654semidirect
980. C2×C3#65944semidirect
988. C5C2×#5654semidirect
1028. C3C2×#65944semidirect
1035. C2#11754826direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×D4×D152
C22×#67822
C2×C5×#9392
C2×C3×#40812
C2×#915732
C2×#915612
C2×#915582
C2×#915562
C22×#66672
C2×#915262
#117548262
C2×#914332
C2×#914202
C2×#914062
C2×#913772
C2×#659443
C2×#56545